IP reputation is a measure of how much wanted mail a particular IP address sends.  This wanted mail is measured as a portion of the total email sent from that IP. Initially IP reputation was really the be all and end all of reputation, there was no real good way to authenticate a domain or a from address. Many ISPs built complex IP reputation models to evaluate mail based on the IP that sent the mail.
These IP reputation models were the best we had, but there were a lot of ways for spammers to game the system. Some spammers would create lots of accounts at ISPs and use them to open and interact with mail. Other spammers would trickle their mail out over hundreds or thousands of IPs in the hopes of diluting the badness enough to get to the inbox. Through it all they kept trying to get mail out through reputable ESPs, either by posing as legitimate customers or compromising servers.
These things worked for a while, but the ISPs started looking harder at the recipient pool in order to figure out if the interactions were real or not. They started looking at the total amount of identical mail coming from multiple IP addresses. The ISPs couldn’t rely on IP reputation so they started to dig down and get into content based filtering.
As the ISPs got better at identifying content and filtering on factors other than source IP, the importance of the IP address on inbox delivery changed. No longer was it good enough to have a high reputation IP sending mail.
These days your IP reputation dictates how fast you can send mail to a particular ISP. But a high reputation IP isn’t sufficient to get all the mail in the inbox. It’s really content that drives the inbox / bulk folder decisions these days.
 
Generally IPs that the ISP has not seen email traffic from before start out with a slight negative reputation. This is because most new IPs are actually infected machines. The negative reputation translates to rate limiting. The rate limiting minimizes people getting spam while the ISP works out if this is a real sender or a spammer.
Some ISPs put mail in the inbox and bulk foldering during the whitelisting process. In this case what they’re doing is seeing if your recipients care enough about your mail to look for it in the bulk folder. If they do, and they mark the mail as “not spam” then this feeds back to the sender reputation and the IP reputation.
If you’re seeing a lot of bulk foldering of mail, it’s unlikely there’s anything IP reputation based to do. Instead of worrying about IP reputation, focus instead on the content of the mail and see what you may need to do to improve the reputation of the domains and URLs (or landing pages) in the emails.

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